Pith Number

pith:3CYLYPAS

pith:2006:3CYLYPASMLNWQX43IEG3DHLEHN

not attested not anchored not stored refs pending

Modified gravity with $f(R) = \sqrt{R^2 - R_0^2}$

Marzieh Farhang, Shant Baghram, Sohrab Rahvar

arxiv:astro-ph/0701013 v1 · 2006-12-31 · astro-ph · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3CYLYPASMLNWQX43IEG3DHLEHN}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Testing Extended Theories of Gravity via Black Hole Photon Rings

Receipt and verification

First computed	2026-07-04T15:16:28.830062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8b0bc3c1262db685f9b410db19d643b612940bd1d1351e3813a5ed9e51fc6de

Aliases

arxiv: astro-ph/0701013 · arxiv_version: astro-ph/0701013v1 · doi: 10.48550/arxiv.astro-ph/0701013 · pith_short_12: 3CYLYPASMLNW · pith_short_16: 3CYLYPASMLNWQX43 · pith_short_8: 3CYLYPAS

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3CYLYPASMLNWQX43IEG3DHLEHN \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d8b0bc3c1262db685f9b410db19d643b612940bd1d1351e3813a5ed9e51fc6de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74a261945e7f1d72530688b3d24e0894f4b9b40617462fec24f2759f5b30ce82",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2006-12-31T07:45:03Z",
    "title_canon_sha256": "a7b7234966905672c91546534de22dbfc562fe8b3d8229ab23bc8158d83f4a1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0701013",
    "kind": "arxiv",
    "version": 1
  }
}